Universität zu Köln

Olivetto, René (2014). Harmonic Maass Forms, Jacobi Forms, and Applications to Lie Superalgebras. PhD thesis, Universität zu Köln.

Preview

PDF PHD-THESIS.pdf - Submitted Version Download (738kB)

Abstract

In this thesis, we prove several results concerning the shape, the modular properties, and the asymptotic behavior of the Fourier coefficients of meromorphic Jacobi forms, with applications to Lie superalgebras. By work of Kac and Wakimoto, Bringmann and Ono, Bringmann and Folsom, and Bringmann, Folsom, and Mahlburg it is known that the generating functions of Kac-Wakimoto characters relative to the $\sl(m|n)^\wedge$ superalgebra are essentially meromorphic Jacobi forms. Extending previous work of Bringmann and Folsom, we investigate Kac-Wakimoto characters for any choice of integers $m>n>0$. Subsequently, we extend the study to any single-variable meromorphic Jacobi form of positive index, and to multivariable Kac-Wakimoto characters. Finally, we investigate the asymptotic behavior of the Fourier coefficients of single-variable Kac-Wakimoto characters using a generalization of the Hardy-Ramanujan Circle Method.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Olivetto, René rene87@live.it UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-58346
Date:	10 July 2014
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language Modular forms , mock modular forms, Jacobi forms, Lie superalgebras, Kac-Wakimoto characters English
Date of oral exam:	1 September 2014
Referee:	Name Academic Title Bringmann, Kathrin Prof. Dr. Zwegers, Sander Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/5835